Generalized Drazin-meromorphic pseudospectrum for multivalued linear relation

Abstract

In this paperwe investigate the spectrum and the Drazin spectrum and their pseudo spectral analogues, for linear relations between Banach spaces and corresponding spectra, the generalized Drazinmeromorphic pseudospectrum. More specifically, the generalized Drazin-meromorphic pseudospectrum for a linear relations on a Banach space is studied. We also make several observations about the level set of the generalized Drazin-meromorphic pseudospectrum of linear relations. Furthermore, it is shown that pseudospectrum has no isolated points, has a finite number of connected components and each component contains an element from the generalized Drazin-meromorphic spectrum.